Newtonian Lubricant Research Articles

Hydrodynamic behaviour of two-phase (liquid-solid) lubricants

An analytical hydrodynamic model was developed to predict the behaviour of a simple two-phase (liquid-solid) lubricant. An experimental study was also carried out with such lubricants using conventional full-film hydrodynamic bearings. Both the analytical and the experimental results showed that the presence of suspended solid particles in a newtonian lubricant enhanced the load-carrying capacity and reduced friction.

Theoretical hydrodynamic load capacity of an axially undefined full porous journal bearing in the turbulent regime considering slip flow and curvature

A mathematical analysis using a new generalized pressure equation is reported for the hydrodynamic lubrication of a 360° long porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. The limiting case of an axially undefined length of the bearing is considered and the axial flow of lubricant in the clearance space is neglected so that the governing differential equation is simpler to solve. Half Sommerfeld boundary conditions are used for the extent of the azimuthal film and film curvature has been included. The curvature effect of the thick porous bearing matrix is taken into account by a new direct approach in which the separation of variables is used for the first time in such a problem. The collocation technique is utilized to determine the hydrodynamic pressure from which the characteristics are evaluated. The results are fully analytical in nature, simple, yet exact and accurate, permitting easy and economical calculation of numerical data over a very wide range of parameters.

Estimation of the performance of a narrow porous journal bearing with hydrodynamic turbulent lubrication considering slip velocity and arbitrary wall thickness

A closed-form mathematical analysis is presented for the hydrodynamic lubrication of a 360° short porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. A new pressure equation is used. The bearing is assumed to be narrow, and therefore circumferential flow of the lubricant in the clearance region is negligible in comparison with that in the axial direction which makes the governing differential equation simpler to solve. However, this simplification is not applicable to darcian flow in the porous matrix so that a three-dimensional Laplace equation is required to describe the continuity of flow in the pores. The film curvature is included by retaining terms containing C R 1 in the expression for film thickness. The curvature of the permeable bearing matrix, which allows it to have an arbitrary wall thickness, is taken into account by a direct approach. Infinite Fourier series and their orthogonal properties are utilized for the determination of the turbulent hydrodynamic pressure distribution from which the load-carrying capacity and attitude angle are calculated. All the results of interest are simple and fully analytical in nature permitting easy and economical calculation of numerical data over a very wide range of parameters.

Thermal analysis of an Eyring fluid in elastohydrodynamic traction

Recent research into elastohydrodynamic (EHD) traction has shown that under high pressure and isothermal conditions the flow properties of typical lubricants follow the Eyring relation between shear stress τ and shear rate /.γ: η/.γ = τ 0sinh( τ τ 0 ) where η is the Newtonian viscosity and τ 0 a representative stress. The maximum in the traction curve arises from shear heating, and Crook's thermal analysis for a Newtonian lubricant has been modified to apply to an Eyring lubricant. In an EHD contact the pressure and hence the viscosity η vary from inlet to outlet, but it is shown that under the conditions of maximum traction it is sufficiently accurate to use the average values of η and τ 0 associated with the average values of pressure and temperature through the length of the contact. A simple formula can then be derived for the maximum traction coefficient in terms of the properties of the fluid (viscosity, pressure and temperature indices, and the representative stress τ 0 and the operating conditions (contact pressure, speed and film thickness).

Steady State Performance of a Hydrodynamic Journal Bearing With a Pseudoplastic Lubricant

Starting from the general shear stress-shear strain relation of the odd cubic polynomial type considering correlation effect for pseudoplastic (shear thinning) lubricant, a modified form of Reynolds’ equation (nonlinear) is derived under conventional hydrodynamic lubrication approximations. The finite difference technique with successive over relaxation is used adopting the solution of the associated linear equation as a first approximation to obtain the pressure distribution of a finite cylindrical journal bearing incorporating Reynolds’ boundary conditions. Steady state performance characteristics such as load capacity, attitude, friction and flow rate are obtained for various values of nonlinear parameter and bearing slenderness ratio. The results presented in nondimensional form are compared with established results for Newtonian lubricants. The investigation shows a significant effect of correlation on the bearing load capacity and flow rate.

The steady state performance of a hydrodynamic journal bearing with a non-newtonian lubricant

Using the Reiner-Philippoff shear stress-shear strain rate relation a modified form of Reynolds equation is derived for a non-Newtonian (shear thinning as well as shear thickening) lubricant under conventional hydrodynamic lubrication approximations. A finite difference iteration scheme with successive over-relaxation incorporating Reynolds boundary conditions is used to obtain the pressure distribution of a cylindrical journal bearing. Steady state performance characteristics such as load capacity, friction and flow rate are obtained for various values of non-linear parameters. The results presented in dimensionless form and applicable to shear-thinning as well as shear-thickening lubricants are compared with established results for New-tonian lubricants.

Lubrication With Micropolar Liquids and Its Application to Short Bearings

Microscopic effects, generated by micromotions of particles in suspension in a viscous fluid, drastically change the character of the flow between solid walls. To the modified momentum and continuity equations, an equation of angular (spin) particle momentum is added. A vectorial system of equations is presented, for variable material coefficients. General properties of this system are discussed and differential equations for pressure and velocity field are derived. For constant viscosity and micropolar coefficients across the lubricating film, important simplifications lead to easier workable expressions. Under this assumption, the short bearing performance has been analyzed. The fluid pressure increase (compared to Newtonian flow) is represented by a surface depending on two groups of micropolar parameters; the overall bearing characteristics also exhibit larger values with respect to simple Newtonian lubricants. However, for similar gap geometries, the friction coefficient has lower values. Some formulas, regarding the velocity field, friction stresses and side flow, are general and may be applied to any bearing length-diameter ratio.

Linearized turbulent lubrication equation for finite self-acting porous bearings considering slip velocity over a hydrodynamically rough permeable boundary

A first attempt to derive a new lubrication equation for the hydrodynamic pressure generation in a three-dimensional self-acting porous metal bearing operating in a turbulent regime (fully developed) with single-phase Newtonian incompressible lubricant is presented considering simultaneously the slip velocity and the hydrodynamically rough permeable surface (in terms of the median diameter of the graded constituent particles of the sintered porous matrix and their standard deviation) with a hydrodynamically rough rotor. The analysis is analogous to boundary layer theory wherein the lubricant motion is treated as a generalized turbulent channel flow in which the rough porous wall is stationary and the impervious wall (also considered rough) is in longitudinal motion so that the flow is a turbulent shear flow coupled with codirectional and transverse turbulent pressure flow. A linearization or perturbation technique is used to decouple the two orthogonal turbulent flows by assuming that the turbulent shear stress in a finite bearing is a small perturbation of the shear stress for turbulent couette flow. Using Boussinesq's eddy viscosity formulation and the experimentally established logarithmic law as the universal law of wall, the governing pressure distribution equation is obtained from consideration of the conservation of momentum and continuity. The whole treatment is approached from the point of view of fluid film design. No ad hoc slip model is used, and the lubrication equation is fully analytical and can be applied to a number of particular bearing problems by applying suitable simplifying restrictive conditions. The derived lubrication equation can be used to predict bearing performance characteristics even in situations where the bearing permeability is non-isotropic.

The simultaneous effects of thermal and inertia on the performance of non-newtonian squeeze films

In the present analysis the interactions of thermal and inertia effects on the performance of non-Newtonian squeeze films have been investigated. The numerical results for pressure drop and inertia correction in load have been obtained and their behaviours are illustrated in figures. The theoretically predicted results of pressure drop for the Newtonian lubricant have also been compared with experimental results of Tichy and Winer which are in close agreement at 70°F to illustrate the importance of the study.

A lubrication equation including slip velocity for hydrodynamic porous bearings in the lower turbulent regime — a perturbation approach

A first attempt is made to analyse pressure development in the form of a new lubrication equation including slip velocity for finite self-acting hydrodynamic porous metal bearings operating in the turbulent regime (fully developed) with a single phase Newtonian incompressible lubricant. The derivation is based on the analogy of boundary layer theory wherein lubricant motion is treated as a generalized turbulent channel flow in which the impermeable wall is in motion and the porous wall is stationary. The type of flow varies from pure couette flow to shear flow coupled with codirectional and transverse pressure flow. A linearization (or perturbation) technique is used to decouple the two orthogonal flows by assuming that the shear stress in a finite bearing is a small perturbation of the shear stress valid for couette flow. Using Boussinesq's eddy viscosity formulation and the wellestablished power law as a universal law of wall, the governing pressure distribution equation is obtained from considerations of the conservation of momentum and continuity. The surfaces are considered to be hydrodynamically smooth. The whole treatment is approached from the viewpoint of fluid film design rather than from a fundamental fluid mechanics approach. No slip model has been used. The lubrication equation is fully analytical and can be applied to a number of particular bearing problems by using the simplifying restrictive conditions. The lubrication equation derived can be used to predict the bearing performance characteristics even in situations where the permeability of the bearings is anisotropic and the Poiseuille flow in the porous matrix does not obey Darcy's law.

A Thermal Hydrodynamic Lubrication Theory for Hydrostatic Extrusion of Low Strength Materials

The paper presents a theoretical analysis of hydrodynamic lubrication in the hydrostatic extrusion process which includes a consideration of thermal effects in the lubricant film arising from the work of plastic deformation. A Newtonian lubricant with an exponential pressure-temperature-viscosity relationship has been assumed and allowance has been made for the effects of redundant deformation of the worked material. The results of the theory are compared with those from previous isothermal and solid friction theories.

Nondimensional Presentation of Frictional Tractions in Elastohydrodynamic Lubrication—Part I: Fully Flooded Conditions

Using several sources, analytic and semi-analytic solutions for frictional tractions of a lubricated line contact are presented in the appropriate non-dimensional form which is similar to that previously used by Moes for film thickness. A Newtonian lubricant with an exponential relationship between viscosity and pressure is assumed and, at this stage, the treatment is confined to fully flooded conditions. The components of frictional tractions arising from rolling (Poisseiulle) and sliding (Couette) flows are distinguished and sliding tractions in the outlet cavitated region are separated from those in the main pressure zone. Three main regimes of lubrication are studied: classical (isoviscous, undeformed), low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The results presented here provide a broad background of approximate results, covering a very wide range of conditions against which the results of more precise computer-based analyses can be judged. Thus the treatment reveals the existence of a range of conditions (typical of the lubrication of glassy polymers by hydrocarbon lubricants) which has been little studied and is, as yet, imperfectly understood.

A Three-Dimensional Thermohydrodynamic Analysis of Sector Thrust Bearings

Equations governing the steady-state thermohydrodynamic behavior of sector-shaped thrust bearings are solved numerically for an incompressible laminar flow of a Newtonian lubricant. The lubricant viscosity is taken as a function of the three-dimensional temperature distribution in the fluid film. Also, a general film thickness profile is allowed. Three dimensional heat transfer between the lubricant and both the moving and stationary solids is included in the analysis. The full thermohydrodynamic solutions are compared with other simpler solutions. It is shown that a type of adiabatic solution allowing for temperature gradients across the film can be used in most cases to predict accurately bearing load, friction, and lubricant flow. The results, expressed in nondimensional terms, can be applied to a wide range of operating conditions.

Possible Role of Compressional Viscoelasticity in Concentrated Contact Lubrication

An equation relating liquid density and viscosity under transient pressure conditions is derived. The derivation combines approximate phenomenological descriptions of the viscoelastic compression of a liquid and the dependence of viscosity on pressure and density. Solutions of the equation for a “step”-pressure increase and a semielliptical pressure cycle show that density and viscosity of Newtonian lubricants may significantly lag pressure transients under concentrated-contact lubrication conditions. Qualitatively, the lag effects appear to account at least partially for anomalous experimental observations involving asperity interactions and elastohydrodynamic lubrication of rollers.

The Rheological Behavior of the Lubricant in the Contact Zone of a Rolling Contact System

A technique has been developed for studying the rheological behavior of the lubricating film within the contact zone of rolling contact bodies. This is accomplished by rolling two contacting disks together with a small amount of sliding superimposed on a relatively high rolling velocity. By measuring the traction, slip-rate, and the lubricant film thickness in the elastically deformed contact, a plot of traction versus mean shear rate can be made. Data are presented for polyphenyl ether. The data depend on the disk temperature and contact pressure qualitatively as would be expected, but the observed dependencies on shear rate and rolling speed require explanation. Analysis of possible local thermal disturbances on the lubricating film assuming a Newtonian lubricant model indicates that, for the experiments described here, temperature changes only partially explain the observed nonlinear variations of traction with shear rate, and fall far short in accounting for variations with rolling speed. A study assuming isothermal conditions and a Ree-Eyring lubricant model provides a traction theory which is flexible enough to fit the variations with shear rate, if certain parameters have advantageous values, but which appears only partially able to correlate the variations with rolling speed. Thus additional analyses which consider, say, both non-Newtonian and thermal effects or perhaps other entities are necessary for interpreting the data.

Conical step bearing using a power law lubricant

In this paper the use of a power law fluid as lubricant in a conical step bearing is considered. The effect of the flow behaviour index on the load capacity is studied, and it is shown that the load capacity can be increased by using a pseudo-plastic fluid as a lubricant rather than a Newtonian lubricant.

Vibration of journal bearings in vacuum : K. E. Demorest and E. C. McKannan, Lubrication eng., 19 (2) (1963) 59–67; 8 fig.

A theoretical study of squeeze film behaviour for a finite journal bearing lubricated with couple stress fluids is presented. On the basis of the microcontinuum theory, the modified Reynolds equation is obtained by using the Stokes equations of motion to account for the couple stress effects due to the lubricant blended with various additives. With the Conjugate Gradient Method of iteration the built-up pressure is calculated, and then applied to predict the squeeze film characteristics of the system. According to the results evaluated, the rheological influence of couple stress fluids is physically apparent. Compared with the case of a Newtonian lubricant, the couple stress effects increase the load-carrying capacity significantly and lengthen the response time of the squeeze film behaviour. On the whole, the presence of couple stresses improves the characteristics of finite journal bearings operating under pure squeeze film motion. The rheological effects of couple stress fluids agree with previous works.

Calculated Performance of Greases in Journal Bearings

A digital computer analysis has been made of the effects of non-Newtonianism on the performance of greases in finite width journal bearings. As anticipated, t he extreme nonlinearity of the shear rate-shear stress relation exhibited by greases makes their deviations from “normal” behavior very marked. Among the effects noted are (1) apparent “anisotropic viscosities,” i.e., viscosities in the side leakage direction as much as 30 times as high as those in the direction of motion, (2) reduced side leakage, (3) flatter pressure profiles, (4) reduced sensitivity of load and friction to speed changes relative to Newtonian lubricants, and (5) the occurrence of “cores” of plug flow. Theoretically interesting is the fact that the apparent axial viscosity approaches the true viscosity while the circumferential viscosity approaches the slope of the flow curve. Many of the conclusions obtained here, especially the advantages of greases at low speeds, are confirmed in practice. Contributed to the American Society of ...

Fluid Lubrication Theory of Roller Bearing—Part I: Fluid Lubrication Theory for Two Rotating Cylinders in Contact

This paper which consists of Parts I and II presents a general and practical fluid lubrication theory of roller bearings lubricated by Newtonian and non-Newtonian lubricants with considerations to the effect of sliding of roller and the influence of unsteady load. In Part I, the fundamental theory for the lubrication between two rotating cylinders in contact has been investigated. The load capacity and friction of a non-Newtonian lubricant, supposed to be a Bingham plastic, coincide approximately at high speed with those of a Newtonian lubricant with viscosity equivalent to the plastic viscosity of the non-Newtonian lubricant. Under unsteady loads, the squeeze action works effectively so that the load capacity increases. The amount of friction is 4/3 and the load capacity is 2/3 in the case of two rotating cylinders in contact involving sliding, compared with that involving no sliding.

Fluid Lubrication Theory of Roller Bearing—Part II: Fluid Lubrication Theory Applied to Roller Bearing

Using the theory for two rotating cylinders in contact obtained in Part I, the fluid lubrication theory of roller bearings for Newtonian and non-Newtonian lubricants was developed in Part II with considerations of the influences of unsteady load and sliding of rollers. It is clarified that the load capacity under unsteady load is generally larger than that under constant basic load and the average friction is nearly equal for both cases. The frictional moment and load capacity for roller bearing including sliding of rollers decrease to 2/3 of the amount of those for roller bearing including no sliding.